If f(x, y) = xy, find the gradient vector ∇f(7, 2) and use it to find the tangent line to the level curve f(x, y) = 14 at the point (7,2)
a. gradient vector
b. tangent line equation

In linear equation , A tree that is 50m tall and is transpiring roughly 90liters of water each day. So  0 calorie will the tree use to transpire this quantity of water .

What is linear equation explain with example?

What makes an equation linear?

Learn more about linear equation

brainly.com/question/11897796

#SPJ4

Answer:Ming pays $25.96 to the cab driver.

Step-by-step explanation:

Ming took a cab across town, his fare of cab = $22.00

He leaves a tip of 18% of total fare = 18% of $22.00

Total amount = (18% of $22) + $22.00

( 18/100× 22) + 22.00

= (0.18 × 22) + 22.00

= 3.96 + 22.00

= $25.96

Ming pays $25.96 to the cab driver.

Answer:

Step-by-step explanation:

the angle of measure 4x + 12 and the angle of measure 64 are Vertically opposite angles then they are equal in measure

therefore

4x + 12 = 64

⇔ 4x = 64 - 12

⇔ 4x = 52

⇔ x = 52/4

⇔ x = 13

Both solutions satisfy the original equation. As a result, there are no extraneous solutions in this case.

To determine the number of extraneous solutions in the given equation, let's simplify it step by step:

Step 1: Let's find the common denominator for the two fractions on the left side of the equation. The common denominator is (2m + 3)(2m - 3).

Step 2: Apply the common denominator to both fractions:

[(2m)(2m - 3)]/[(2m + 3)(2m - 3)] - [(2m)(2m + 3)]/[(2m + 3)(2m - 3)] = 1

Step 3: Simplify the numerators:

\([4m^2 - 6m - 4m^2 - 6m]/[(2m + 3)(2m - 3)] = 1\)

[-12m]/[(2m + 3)(2m - 3)] = 1

Step 4: Cancel out common factors:

-12m = (2m + 3)(2m - 3)

\(-12m = 4m^2 - 9\)

Step 5: Rearrange the equation:

\(4m^2 + 12m - 9 = 0\)

Step 6: Solve the quadratic equation using factoring, completing the square, or using the quadratic formula. Let's use the quadratic formula:

\(m = (-b ± √(b^2 - 4ac))/(2a)\)

For our equation, a = 4, b = 12, and c = -9. Substituting these values:

m = (-(12) ± √((12)^2 - 4(4)(-9)))/(2(4))

m = (-12 ± √(144 + 144))/(8)

m = (-12 ± √288)/8

m = (-12 ± 12√2)/8

Simplifying further:

m = (-3 ± 3√2)/2

So, we have two potential solutions for m:

m = (-3 + 3√2)/2  and  m = (-3 - 3√2)/2

Now we need to check if these solutions satisfy the original equation. Let's substitute these values back into the equation:

For m = (-3 + 3√2)/2:

[(2(-3 + 3√2))/(2(-3 + 3√2) + 3)] - [(2(-3 + 3√2))/(2(-3 + 3√2) - 3)] = 1

Simplifying this equation, we find that it holds true.

For m = (-3 - 3√2)/2:

[(2(-3 - 3√2))/(2(-3 - 3√2) + 3)] - [(2(-3 - 3√2))/(2(-3 - 3√2) - 3)] = 1

Simplifying this equation, we also find that it holds true.

Therefore, both solutions satisfy the original equation. As a result, there are no extraneous solutions in this case.

To know more about solutions check the below link:

https://brainly.com/question/29174899

#SPJ4

No . of girls in Ms. Jeffry's environmental club = 6

No . of boys in Ms. Jeffry's environmental club = 12

To find the maximum number of groups she can make , we have to find the highest common factor ( HCF ) of the number of boys and girls in her club .

Factors of 6 = 1 , 2 , 3 and 6

Factors of 12 = 2 , 3 , 4 , 6 and 12

Hence the highest common factor of 6 and 12 are 6 .

Therefore , the maximum number of groups Ms . Jeffry can make where the number of girls and boys are same are 6 .

Answer:

14/72

Step-by-step explanation:

Just line them all up and multiply numerators with numerators and denominators with denominators. You have your answer.

Answer: 6 days and 18 hours

Step-by-step explanation: 9/4=1.25 1.25x3=6.75 and so on

Answer:

b.

\( {4}^{15} \times {5}^{10} \)

Step-by-step explanation:

In the given expression u can bring the 5^-2 in the neumerator making it 5^2.

Then multiply both powers by 5.

This algebraic expression represents the same mathematical relationship as the original English phrase.

To translate the English phrase "the quotient of the product of 6 and 6r, and the product of 8s and 4" into an algebraic expression, we need to first identify the mathematical operations involved and then convert them into symbols.

The phrase is asking us to divide the product of 6 and 6r by the product of 8s and 4. In mathematical terms, we can represent this as:

(6 × 6r) / (8s ×4)

Here, the symbol "*" represents multiplication, and "/" represents division. We multiply 6 and 6r to get the product of 6 and 6r, and we multiply 8s and 4 to get the product of 8s and 4. Finally, we divide the product of 6 and 6r by the product of 8s and 4 to get the quotient.

We can simplify this expression by dividing both the numerator and denominator by the greatest common factor, which in this case is 4. This gives us the simplified expression:

(3r / 2s)

for such more question on algebraic expression

https://brainly.com/question/4344214

#SPJ11

The English phrase "the quotient of the product of 6 and 6r, and the product of 8s and 4" can be translated into an algebraic expression as follows: (6 * 6r) / (8s * 4)

Let's break down the expression:

Therefore, the complete expression becomes: 36r / 32s

In this expression, the product of 6 and 6r is calculated first, which is 36r. Then the product of 8s and 4 is calculated, which is 32s. Finally, the quotient of 36r and 32s is calculated by dividing 36r by 32s.

This expression represents the quotient of the product of 6 and 6r and the product of 8s and 4. It signifies that we divide the product of 6 and 6r by the product of 8s and 4.

In algebra, it is important to accurately represent verbal descriptions or phrases using appropriate mathematical symbols and operations. Translating English phrases into algebraic expressions allows us to manipulate and solve mathematical problems more effectively.

To learn more about algebraic expressions, click here: https://brainly.com/question/4344214

#SPJ11

The point where the line intersects the plane is (-8/3, 11/3, 8/3).

To find the point where the given line intersects the plane, we need to find values of t that satisfy both the equation of the line and the equation of the plane.

First, we can substitute the equations of  line into the equation of the plane to get:

3(-1-t) + (2+t) + 3(1+t) = 1

Simplifying this equation gives:

-3t + 6 = 1

-3t = -5

t = 5/3

Now that we have found a value of t that satisfies both equations, we can substitute it back into the equation of the line to get the point of intersection:

x = -1 - (5/3) = -8/3

y = 2 + (5/3) = 11/3

z = 1 + (5/3) = 8/3

Learn more about intersection here

brainly.com/question/118569

#SPJ4

The given question is incomplete, the complete question is:

How to find the point where the line x = –1 – t, y = 2 + t, z = 1+ t intersects the plane 3x + y + 3z = 1 ?

Rule for a dilation with center (0,0)

k is the scale factor.

For point P (0,3):

The slope y-intercept form of a linear equation is given as y = mx +c so for 13,14,15,16 the equations are y = 2x - 5,y = -x - 5,y = -x/2 + 1, and y = 3x/4 - 2 respectively.

A linear function is a function that varies linearly with respect to the changing variable.

A linear function always has the same and constant slope.

In the 13 figure,

The linear equation of a line is ,

y = mx + c where m is the slope while c is the y-intercept.

The slope associated with two points (x₁, y₁) and (x₂, y₂) is given by

Slope(m) = (y₂ - y₁)/(x₂ - x₁)

So, the slope associated with points (3,1) and (1,-3) is,

m = (-3 - 1)/(1 - 3) = 2

So, y = 2x + c

Now substitute,(3,1)

1 = 2(3) + c

c = -5

So the b becomes, y = 2x - 5.

With the same approaches, the equations for the 14,15, and 16 figures are y = -x - 5,y = -x/2 + 1, and y = 3x/4 - 2 respectively.

Hence "The slope y-intercept form of a linear equation is given as y = mx +c so for 13,14,15,16 the equations are y = 2x - 5,y = -x - 5,y = -x/2 + 1, and y = 3x/4 - 2 respectively".

For more about the linear function,

brainly.com/question/21107621

#SPJ1

There are 172 boys in the introductory geology course.

The ratio of boys to girls is 4:5. We can know that the number of boys in the class is four multiplied by the common value that the ratio is based on.

We can call this usual value x and say that the number of boys in the class is 4x. Applying the same logic to the girls, we can say that there are 5x girls in the class. Hence, a total of 9x children. We divide the total value by 9 to get x, which equals 43.

We can then calculate the number of boys by calculating 4x, which equals 172.

To know more about Geology Course:

https://brainly.com/question/30355289

#SPJ4

The sample size required in this case is 71 pupils, which must be tested in order for the margin of error to be equal to 3 points.

When it comes to statistics, selecting a relatively small representative sample and conducting hypothesis testing on it typically makes it easier to analyze a large population. By boosting the sample size, the margin of error, which represents the sampling procedure's statistical precision, can be decreased.

From standard normal tables,

P( -2.326 < Z < 2.326) = 0.98 here

The sample size required here is computed as:

n = [(z * α) / МОЕ]² = [(2.326 * 18) / 5]² = 70.12

Therefore, the required sample size, in this case, is 71.

To ensure that the margin of error is equivalent to 3 points, 71 students must be assessed.

To know more about Sample Size, refer to this link:

https://brainly.com/question/12995426

#SPJ4

COMPLETE QUESTION:

An IQ test is designed to have scores that have a standard deviation of a 10. A simple random sample of students at a torgo university will be given the test in order to construct a 95% confidence interval for the mean 10 of all students at the university. How many students must be tested so that the margin of error will be equal to 3 points? The sample size required for the desired margin of error is.(Round your answer to next whole number.)

Answer:This is the best i can do for u, Approximately 20% of the time, a driver on their own uses the lane however. During a survey by the Ministry of Transportation 60 cars are selected at random.

Step-by-step explanation:

Answer:

approximately 0.0969

Step-by-step explanation:

Well this is quite tricky but, to determine if the normal approximation is appropriate, we need to check if the conditions for using the normal distribution are met. The conditions are:

The sample size is large enough, typically n ≥ 30.

The sample is drawn at random.

The observations are independent of each other.

The population distribution is approximately normal or the sample size is large enough that the central limit theorem applies.

So, in this case, we are given that 60 cars are selected at random, so the first condition is satisfied.

The second and third conditions are assumed since we are not given any information to suggest otherwise. The fourth condition is more difficult to assess, as we do not know the population distribution of cars using the HOV lane. However, we can use the rule of thumb that if the sample size is large enough (n ≥ 30), the central limit theorem applies and we can use the normal distribution to model the sample proportion.

So, we can conclude that the normal approximation is appropriate for this situation.

Let p be the proportion of cars that have less than 2 people in them. We are given that approximately 20% of the time, a driver on their own uses the HOV lane, which means that p = 0.2.

We want to find the probability that exactly 10 cars have less than 2 people in them. Let X be the number of cars with less than 2 people in them, then X follows a binomial distribution with parameters n = 60 and p = 0.2. We can use the normal approximation to the binomial distribution, which is:

X - N(np, np(1-p)

So, the mean and standard deviation of X are:

mean = np = 60 × 0.2 = 12

standard deviation = sqrt(np(1-p)) = sqrt(60 × 0.2 × 0.8) = 2.19

To find the probability that exactly 10 cars have less than 2 people in them, we need to find the probability that X = 10:

P(X = 10) = P(9.5 ≤ X ≤ 10.5) (using continuity correction)

We can standardize the distribution to a standard normal distribution:

z = (X - mean) / standard deviation = (10 - 12) / 2.19 = -0.91

P(9.5 ≤ X ≤ 10.5) = P(-0.91 ≤ z ≤ -0.46) (using the standard normal distribution table or calculator)

Looking up the standard normal distribution table or using a calculator, we find that P(-0.91 ≤ Z ≤ -0.46) = 0.0969.>>

So therefore, the probability that exactly 10 cars have less than 2 people in them is approximately 0.0969..

Answer:

13

Step-by-step explanation:

5^2 + 12^2 = Y

Sqrt Y = X

K is therefore equal to 1/2 since in the right-angled triangle, one angle is 45 and the perpendicular is 10 cm.

Since a triangle has three sides and three vertices, it is a polygon. It is a fundamental geometric shape. Triangle ABC is the moniker given to a triangle that has vertices A, B, and C. When the three points are not collinear, a singular plane and triangle are found in Euclidean geometry. A triangle is a polygon if it has three sides and three corners. The points where the three sides meet are known as the triangle's corners.

given

If you have an angle and its opposite side, you may calculate the hypotenuse by dividing the length of the opposing side by sin().

To find the length of the side next to the angle, you can also divide the length by tan().

Let the hypotenuse be AC=x

Now given AB=Kx

In △ABC

sin45 ∘ = AC / AB

1/2 = kx/x

K= 1/2

K is therefore equal to 1/2 since in the right-angled triangle, one angle is 45 and the perpendicular is 10 cm.

To know more about triangle visit:

https://brainly.com/question/2773823

#SPJ1

Therefore, the area of the pentagon is 928 square units.

Length is a measure of the size or extent of an object or a distance between two points. It refers to the longest dimension of an object or the distance between two points in space, typically measured in units such as inches, centimeters, meters, or miles. In mathematics, length is also used to describe the size of a line segment or a curve, which can be measured using various techniques such as Euclidean distance, arc length, or fractal dimension. Length is an important concept in many fields, including physics, engineering, geometry, and statistics.

Find the area.

Pentagon

apothem = 16 side = 23.2

Note: When necessary, enter your answer as a decimal If it is not a terminating decimal, round to the nearest hundredth

For the first question, we need more information to find the area of the triangle. Knowing the apothem and one side is not enough. We also need to know the number of sides of the triangle or the length of another side or the height.

For the second question, the formula to find the area of a regular pentagon is:

Area = (perimeter x apothem)/2

Since we are given the apothem and the side, we can find the perimeter of the pentagon as:

perimeter = 5 x side = 5 x 23.2 = 116

Substituting the values in the formula, we get:

Area = (116 x 16)/2 = 928

Therefore, the area of the pentagon is 928 square units.

To know more about perimeter visit:

https://brainly.com/question/9369181

#SPJ1

Answer:

\(i \: think \: no \:{{b}}\)

B IS YIHR ANSWER

I HOPE IT HELPS

HAVE A NICE DAY

#Captainpower

A unbiased estimator is a statistic that accurately reflects the population mean, μ. A statistic is unbiased when the mean of its sampling distribution is equal to μ.

Mathematically, this can be expressed as:

E(x) = μ

Where E(x) is the expected value of x and μ is the population mean.

This means that if we take a sample from a population and calculate the mean from that sample, the expected value of that mean should be equal to the population mean. This can be seen in the following example:

Let's say we have a population with a mean of 30. We take a sample of size 5 from this population and calculate the sample mean, x. The expected value of x should be equal to 30. We can calculate this using the formula:

E(x) = ∑xi/n

Where xi are the values in the sample and n is the sample size.

For our example, E(x) = (30 + 30 + 30 + 30 + 30) / 5 = 30

This shows that x is an unbiased estimator of μ.

Learn more about sample mean here:

https://brainly.com/question/30112112

#SPJ4

Rational numbers are numbers that can be absolutely determined. This includes integers, limited decimals, repeating decimals, and fractions. Examples include 1, 1.25, 1.38383838..., and 1/2. Irrational numbers are numbers that cannot have their absolute value determined. This excludes every example for rational numbers. An example of an irrational number is 3.1415926535879... (pi) or 1.41421356237... (sqrt2)

The 8-puzzle problem can be categorized as a "Pathfinding problem."

The 8-puzzle is a classic problem in artificial intelligence and computer science. It involves a 3x3 grid with eight numbered tiles and one empty space. The objective is to rearrange the tiles from an initial configuration to a goal configuration by sliding them into the empty space.

The reason why the 8-puzzle problem is classified as a pathfinding problem is that it involves finding a sequence of moves or actions to reach a desired state or goal. In this case, the desired state is the goal configuration of the puzzle. The problem requires determining the optimal sequence of moves that lead to the goal state while considering the constraints and limitations of the puzzle.

Pathfinding problems involve finding the shortest or optimal path from a starting point to a goal or destination. In the 8-puzzle problem, the empty space serves as the movable "agent" that can slide adjacent tiles. The objective is to find the shortest sequence of moves or actions to transform the initial configuration into the goal configuration, effectively finding a path to the solution.

Therefore, due to its nature of finding an optimal sequence of moves to reach a goal state, the 8-puzzle problem can be categorized as a pathfinding problem.

Learn more about limitations here:

brainly.com/question/12207539

#SPJ11

Answer:

$9 each

Step-by-step explanation:

1.50 x 6 = 9, so c (canvases) are 9 dollars and p (paintbrushes) are 1.50

(what were the "which of the following" options?)

Answer:

the answer is 9

$1.50 +  $1.50 +  $1.50 + $1.50 +  $1.50 +  $1.50 = 9

Step-by-step explanation:

Answer:

130°

Step-by-step explanation:

∠BXF = ∠BXA + ∠AXF  = 90° +40°= 130°

see ∠AXF =∠CXD  opposite angles

∠CXD = 90°  given

∠BXA = 40°  given

The line that passes through (-9,7) and (18,7) has an equation of y = 7. This is because both points have the same y-coordinate of 7, indicating that they lie on a horizontal line.

Therefore, the equation of the line is y = 7.Short answer: The line is a horizontal line with equation y = 7.Long answer: To find the equation of the line that passes through (-9,7) and (18,7), we can use the slope-intercept form of a line which is y = mx + b, where m is the slope and b is the y-intercept.

To find the slope, we can use the formula:m = (y2 - y1) / (x2 - x1)where (x1, y1) and (x2, y2) are the coordinates of the two points.(x1, y1) = (-9, 7) and (x2, y2) = (18, 7), so we have:m = (7 - 7) / (18 - (-9)) = 0 / 27 = 0Since the slope is 0, the line is horizontal. To find the y-intercept, we can substitute one of the points into the equation:y = mx + b7 = 0x + b7 = bTherefore, the equation of the line that passes through (-9,7) and (18,7) is:y = 7

To know more about horizontal line visit:

https://brainly.com/question/2514839

#SPJ11

It is necessary to clean the measuring instrument the moving parts of the measuring device may be harmed if airborne dust or dirt gets inside of it. Additionally, if any foreign objects are present between the measurement target and the measuring device, precise measurements may be affected.

A measuring instrument is a tool used to quantify anything tangible. The act of obtaining and comparing physical amounts of actual objects and occurrences is known as measuring in the physical sciences, quality control, and engineering. Vernier calipers, micrometers, dial gauges, gauges of various types, bubble levels, protractors, and rulers are some of the primary goods that fall under the category of measurement instruments. These equipment are employed in the production process and for quality assurance.

It is necessary to clean the measuring instrument the moving parts of the measuring device may be harmed if airborne dust or dirt gets inside of it.

To know more about measuring instrument visit:-

https://brainly.com/question/525672

#SPJ4

False. The complement of an event A, denoted by A', is the event consisting of all outcomes in the sample space S that are not in A.

In probability theory, a sample space S represents the set of all possible outcomes of an experiment or random phenomenon. An event A is a subset of the sample space S, representing a specific outcome or a combination of outcomes of interest.

The complement of event A, denoted by A', includes all the outcomes in the sample space S that are not part of event A. In other words, A' consists of all outcomes that do not satisfy the conditions for event A to occur.

For example, let's consider rolling a fair six-sided die. The sample space S consists of the numbers {1, 2, 3, 4, 5, 6}. Now, let event A be the event of rolling an odd number. In this case, A = {1, 3, 5}, and the complement of A, denoted by A', would be A' = {2, 4, 6}. A' includes all the outcomes that are not odd numbers.

It's important to note that the complement of an event A and the event itself together cover the entire sample space S. In other words, A and A' are mutually exclusive and exhaustive, meaning that any outcome must either be in A or in A'.

So, in summary, the complement of an event A is the set of all outcomes in the sample space S that do not belong to A.

To know more about probability theory refer here:

https://brainly.com/question/31469353

#SPJ11

The initial value in this equation is the constant term, which is 15 dollars. This is the fixed monthly charge, regardless of how many minutes are used.

The given formula is: C(n) = 15 +0.04n, where n is the number of minutes talked, and C(n) is the monthly charge, in dollars. This formula represents the monthly cost of a phone service that charges a fixed monthly fee of 15 dollars plus an additional fee of 0.04 dollars per minute for the number of minutes talked.

The rate of change of this formula is the derivative of C(n) with respect to n, which is the coefficient of n, in this case, 0.04. This means that for each additional minute used, the monthly cost increases by 0.04 dollars. For example, if a customer uses 100 extra minutes in a month, their monthly charge would increase by 0.04 * 100 = 4 dollars.

The initial value in this equation is the constant term, which is 15 dollars. This is the fixed monthly charge that the customer pays regardless of how many minutes are used. Even if the customer doesn't make any calls, they would still be charged a minimum of 15 dollars per month.

In summary, the rate of change in this formula is 0.04 dollars per minute, and the initial value is 15 dollars. These values can be useful in calculating the total cost of the phone service for a given number of minutes used or in comparing this service to other phone plans with different rates and initial values.

To learn more about  initial value visit:https://brainly.com/question/13243199

#SPJ11